What Is the Way to Solve "ln(e^2)"?


Quick Answer

To solve ln(e^2), a person can use a graphing calculator or can calculate by hand using substitution methods The final answer of ln(e^2) is 2.

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Full Answer

Substitution methods begin by allowing both sides to be exponents of the base e. Another example is ln(x) = 8. This can be rewritten as e^ln(x) = e^8 when both sides are exponents of the base e. When the base of an exponent and the base of a logarithm are the same then the left side can be written as x so this equation could now be written as x = e^8. This provides the answer, which is x is approximately 2,980.95798704.

When working within logarithms and natural logarithms, there are important rules to keep in mind. One is that the definition of a natural logarithm is e^y = x. The base e logarithm of x is ln(x) = loge(x) = y. The e constant is approximately 2.71828183.

There are also various rules that are used to determine logarithms. The logarithm product rule is logb(x times 7) = logb(x) + logb(y). The logarithm quotient rule is logb(x/y) = logb(x) - logb(y). The logarithm power rule is lob(x^y) = y times logb(x). These rules can used when solving problems that include logarithms. It is also important to remember that when x is equal to zero, the ln(x) is undefined.

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